Multimodal multi-objective optimization based on local optimal neighborhood crowding distance differential evolution algorithm.

In practical applications, the optimal solutions of multi-objective optimization are not unique. Some problems exist different Pareto Sets (PSs) in the decision space mapped to the same Pareto Front (PF) in the objective space, which are called multimodal multi-objective problems (MMOPs). To tackle this issue, this paper proposes a multimodal multi-objective optimization based on a local optimal neighborhood crowding distance differential evolution algorithm. First, an adaptive partitioning strategy in the initialization phase is proposed by using the characteristics of the heuristic stochastic search. That ensures the local optimal solution is quickly found among multiple PSs. Second, opposition-based learning is combined with differential mutation to generate vectors, which accelerate the convergence of the population to the optimal solution. Finally, a method for neighborhood crowding distances on different Pareto ranks is designed. The distance is computed by a weighted sum of Euclidean distances for the nearest neighbors. While reducing computational complexity, this strategy reflects realistic crowding degree. With these methods, balances the diversity performance of the decision and the objective space, while improving the search capability. Multiple PSs reveal the problem's potential characteristics and meet the needs of the decision-maker. The practical significance is verified by the application of actual distance minimization problem. According to experimental results, the proposed method can achieve a high level of comprehensive performance. [ABSTRACT FROM AUTHOR]